Sam Allardyce may feel comfortable with his place in West Ham’s history but afternoons like this do not offer great hope of an enduring legacy with Sunderland. This was a low-key return to the ground that Allardyce called home for four years, any thoughts of a hot reception quickly fading away in a lunchtime fug, but his current side created enough chances to equalise Michail Antonio’s first-half goal and if Sunderland cannot find a cutting edge soon then their mini revival since the New Year may come to nought. West Ham move fifth for at least 24 hours; for Allardyce’s strugglers, a sense of urgency now envelops Tuesday’s home match with Crystal Palace.

Perhaps it was bad luck for Allardyce that the two best opportunities, both in the last 16 minutes, fell to Jack Rodwell. The midfielder last scored in the league a year ago but it was he, found 10 yards out by DeAndre Yedlin’s accurate cutback, who placed his shot too close to Adrian’s legs and who, shortly afterwards, saw Sam Byram get enough of a block in to atone for his own mistake when a goal seemed certain. Jermain Defoe also missed a presentable chance shortly after a turgid opening period, volleying wide after James Collins had misjudged a Lee Cattermole punt, and his manager was visibly frustrated afterwards.

“It’s a huge disappointment not to have picked up any points,” Allardyce said. “We came off after creating chances [and losing 1-0] against Man City at home and we’re kicking ourselves again today. It’s worrying me a great deal, because somewhere along the line you won’t play as well as that. I thought we did enough to win it, let alone draw it.”

That was a generous assessment, but Allardyce presumably knew he had caught West Ham on an off day. His delayed arrival on the touchline, whether staged or otherwise, had been met with utter indifference and the match had begun in a similarly inert vein, lit finally by Vito Mannone’s reflexes in tipping a 20-yard Mark Noble drive on to the crossbar. An angled Wahbi Khazri free-kick that flicked the opposite frame was Sunderland’s riposte but the winning goal, scored on the half-hour, owed plenty to the inattention behind what is now a 13-game run without a clean sheet.

Patrick van Aanholt, a left-back who tends to look far more comfortable on the front foot, should have cleared a straightforward ball out of sight but instead presented it straight to Antonio. The winger’s finish, curled left-footed past a possibly unsighted Mannone, was clinical but he was aided by the lack of resistance offered by either Van Aanholt or the covering Dame N’Doye.

West Ham were content to play on the counter thereafter although Antonio was thwarted by Mannone before half-time and the substitute Andy Carroll became the third player to hit the bar between Rodwell’s two sights of goal. “We’re West Ham United, we play on the floor”, had been the home crowd’s only real attempt at riling Allardyce but this became an afternoon for getting the job done by more artisanal means.

West Ham’s manager Slaven Bilic said: “In the hotel and dressing room before the game we were all up for it, but at half time I told the guys we were not flat, but not in the red zone. The crowd also were a little bit sleepy, maybe because it was an early kick-off. We knew it was going to be hard, but we weren’t in that zone and it makes this win even bigger for us.”

It was one of Dimitri Payet’s quieter days, other than a half-chance struck over in the second period. There was, though, encouragement in a productive first start since 2 January for Manuel Lanzini and Bilic rejected the idea his side had been forced to ride their luck.

“We created more chances, scored the goal and hit the post twice,” he said. “There’s always the danger that you are going to concede. They created some chances in the second half but if you are trying to tell me they deserved to win the game, no way. Every team that plays today and goes 1-0 down will get chances to equalise.”

Another of Sunderland’s openings had fallen to the mercurial Khazri, who got to the byline in the 87th minute only to fall on his backside attempting an unnecessary rabona. “I can’t comment on that because I might say something I regret,” Allardyce said. No hero’s welcome; no heroics on the pitch. It had been that kind of afternoon for him.